Boxplot diversity predicted by mountain. Does it look like there are differences between mountains? Fit a simple linear model predicting diversity from mountain. Is it significant? What is the p-value? Is this test valid? Why/why not?

Calculate the mean diversity for each mountain and the mean height for each mountain. Plot these mean heights (on the x-axis) against these mean diversities (on the y-axis). Does it look like there is a relationship? Positive or negative? Fit a simple linear model predicting mean diversity from mean height. Is it significant? What is the p-value? Does the fitted model indicate a positive or negative relationship (whether significant or not)? Is this test valid? Why/why not?

Use the 'aov' and 'Error' functions to fit a linear model predicting diversity in terms of height, but with a random effect for mountain. Is height a significant predictor of diversity? What is the p-value? Does the fitted model indicate a positive or negative relationship (whether significant or not)? Is this test valid? Why/why not?

Use the 'lme' function from the 'nlme' library to fit a linear model predicting diversity in terms of height, but with a random effect for mountain. Is height a significant predictor of diversity? What is the p-value? Does the fitted model indicate a positive or negative relationship (whether significant or not)? Is this test valid? Why/why not?

Plot the height of all the sites against their diversity again, but this time using a different colour and/or symbol for each mountain. Hopefully this will help you understand the results of the previous tests better. Make any other plots you think will help. Write down your conclusions from the analysis and plotting that you have done.

show in R

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	mountain	height	diversity
1	1	1397	5.10037248
2	1	1447	5.169128411
3	1	1497	5.315592543
4	1	1547	5.177057709
5	1	1597	5.246577868
6	1	1647	5.281062346
7	1	1697	5.348938721
8	1	1747	5.345864366
9	1	1797	5.592990271
10	1	1847	5.591565928
11	2	1125	4.064557011
12	2	1175	4.254151531
13	2	1225	4.023241341
14	2	1275	4.257306765
15	2	1325	4.065559655
16	2	1375	4.196965278
17	2	1425	4.276771736
18	2	1475	4.367977778
19	2	1525	4.521547563
20	2	1575	4.715540482
21	3	1854	2.409447387
22	3	1904	2.42781485
23	3	1954	2.523035086
24	3	2004	2.557915967
25	3	2054	2.685482283
26	3	2104	2.754000386
27	3	2154	2.926928154
28	3	2204	2.878846944
29	3	2254	2.98873069
30	3	2304	2.997361575
31	4	1049	5.495168549
32	4	1099	5.299676333
33	4	1149	5.3849464
34	4	1199	5.57548318
35	4	1249	5.415983462
36	4	1299	5.715199596
37	4	1349	5.81696049
38	4	1399	5.652003601
39	4	1449	5.992316574
40	4	1499	5.819080228
41	5	1538	3.600380009
42	5	1588	3.79203119
43	5	1638	3.650732871
44	5	1688	3.706923393
45	5	1738	3.893513503
46	5	1788	3.795189187
47	5	1838	3.935849493
48	5	1888	4.124001086
49	5	1938	4.089768631
50	5	1988	4.183277771
51	6	1300	4.091504742
52	6	1350	4.389419798
53	6	1400	4.289918769
54	6	1450	4.581089593
55	6	1500	4.430968777
56	6	1550	4.541482325
57	6	1600	4.774967853
58	6	1650	4.577182828
59	6	1700	4.557348396
60	6	1750	4.749631977
61	7	1456	2.971385146
62	7	1506	3.169863357
63	7	1556	3.136098295
64	7	1606	3.090004472
65	7	1656	3.300534392
66	7	1706	3.232520914
67	7	1756	3.284875975
68	7	1806	3.375392182
69	7	1856	3.541080419
70	7	1906	3.444340028
71	8	1104	3.205745648
72	8	1154	3.170161572
73	8	1204	3.240935265
74	8	1254	3.48024155
75	8	1304	3.43843938
76	8	1354	3.385784545
77	8	1404	3.393048218
78	8	1454	3.53943294
79	8	1504	3.713257708
80	8	1554	3.835599143
81	9	1190	0.146996667
82	9	1240	0.0167
83	9	1290	0.322545564
84	9	1340	0.22237927
85	9	1390	0.353891635
86	9	1440	0.346103561
87	9	1490	0.373726419
88	9	1540	0.685251261
89	9	1590	0.618874736
90	9	1640	0.675604601
91	10	1596	4.899698869
92	10	1646	4.893264273
93	10	1696	5.008870991
94	10	1746	5.11899002
95	10	1796	5.256239126
96	10	1846	5.19565136
97	10	1896	5.203179606
98	10	1946	5.388051331
99	10	1996	5.438019672
100	10	2046	5.342328151
101	11	1542	3.200496592
102	11	1592	3.144065784
103	11	1642	3.240638339
104	11	1692	3.347774257
105	11	1742	3.283044604
106	11	1792	3.592641541
107	11	1842	3.453060046
108	11	1892	3.703895282
109	11	1942	3.611722457
110	11	1992	3.46751941
111	12	1699	1.494260172
112	12	1749	1.60237296
113	12	1799	1.685562581
114	12	1849	1.628970299
115	12	1899	1.782198633
116	12	1949	1.712237307
117	12	1999	1.878982163
118	12	2049	1.801840062
119	12	2099	1.913595992
120	12	2149	2.019894616
121	13	1114	4.15479007
122	13	1164	4.212348018
123	13	1214	4.183019194
124	13	1264	4.415957332
125	13	1314	4.496069478
126	13	1364	4.357688005
127	13	1414	4.432555632
128	13	1464	4.693619147
129	13	1514	4.683713358
130	13	1564	4.724482002
131	14	1389	2.936016484
132	14	1439	2.84110802
133	14	1489	3.078994297
134	14	1539	2.910325658
135	14	1589	3.184465062
136	14	1639	3.25945566
137	14	1689	3.363527403
138	14	1739	3.417213355
139	14	1789	3.525380606
140	14	1839	3.339822934
141	15	1702	2.079239241
142	15	1752	2.25988139
143	15	1802	2.216739954
144	15	1852	2.26757503
145	15	1902	2.404643749
146	15	1952	2.427398494
147	15	2002	2.551152598
148	15	2052	2.626579379
149	15	2102	2.710472634
150	15	2152	2.813699199
151	16	1311	3.66127784
152	16	1361	3.688161472
153	16	1411	3.719858948
154	16	1461	4.068102752
155	16	1511	3.982687802
156	16	1561	4.070708957
157	16	1611	3.928538035
158	16	1661	4.284122624
159	16	1711	4.179488254
160	16	1761	4.084108638